The sum of two numbers is $101$, and their difference is $33$. What are the two numbers?
Explanation: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 101}$ ${x-y = 33}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 134 $ $ x = \dfrac{134}{2} $ ${x = 67}$ Now that you know ${x = 67}$ , plug it back into $ {x+y = 101}$ to find $y$ ${(67)}{ + y = 101}$ ${y = 34}$ You can also plug ${x = 67}$ into $ {x-y = 33}$ and get the same answer for $y$ ${(67)}{ - y = 33}$ ${y = 34}$ Therefore, the larger number is $67$, and the smaller number is $34$.